We expect the participants to have basic knowledge in classical and statistical mechanics, thermodynamics, and partial differential equations, as well as knowledge of a programming language (Python or C).

The lecture is accompanied by hands-on-tutorials which will take place in the CIP-Pool of the ICP, Allmandring 3. They consist of practical exercises at the computer, like small programming tasks, simulations, visualization and data analysis.
The tutorials build upon each other, therefore continuous attendance is expected.

Lecture

Scope

The first part of the course intends to give an overview about modern simulation methods used in physics today. The lecture should introduce different approaches to simulate a physical systems. In this respect, rather a broad range of methods will be outlined than an exhaustive presentation of specific computational methods. Roughly, the lecture will consist of:

General overview

The first 2-3 weeks will be dedicated on the general common aspects of computer simulations, elements of statistical ensemble theory and elements of elasticity theory, which are essential in understanding and performing simulations.

Quantum Mechanics

An extensive presentation of quantum mechanical simulations will be given in the second part of this course. Here, a general overview of the ideas behind these kinds of simulations will be given.

Molecular Dynamics

A more extensive investigation of classical Molecular Dynamics (MD) simulations is planned. This includes the algorithm, the integrators, the thermostats, to name a few necessary to perform MD simulations.

In terms of the respective tutorials, the goal is to be able to set up and run real MD simulations for different ensembles and understand and interpret the output.

Monte Carlo Simulations

A part of the lecture will be dedicated on Monte Carlo (MC) methods and their algorithms. Specific examples, such as the Ising model will be studied.

Error Analysis

The way errors come into the simulations and how to estimate these will be outlined.<-!!Autocorrelation, Jackknifing, Bootstrapping-->

Potentials

An important component of molecular simulations are the potentials or force fields chosen to model the interactions within the simulated system. The efficiency of the simulations is stongly dependent on this choice. To this purpose, various methods can be applied for obtaining efficient potentials for different methods. Here, representative examples will be outlined.

Simulation of liquids

Methods such as the lattice Boltzmann method and specific details on simulating liquids will be briefly given.

Advanced simulation techniques

In the end of the course, a short overview of other more advanced methods than the ones studied here will be presented. Examples include MC beyond the Metropolis algorithm, metadynamics or rare events sampling.

Prerequisites

We expect the participants to have basic knowledge in quantum, classical and statistical mechanics, thermodynamics, electrodynamics, and partial differential equations, as well as knowledge of a programming language.

Certificate Requirements

1. Attendance of the exercise classes

2. Obtaining 50% of the possible marks in the hand-in exercises

There will be a final grade for the Module "Simulation Methods" (this module consists of both lectures, Sim I plus Sim II) determined at the end of lecture Simulation Methods II.

The final grade will be determined in the following way: There will be an oral examination performed at (or after) the end of the course Simulation Methods II (SS 2012).